As it was detailed in [1]}, we can solve the differential equation, Eq. (REF ), for the map \(\phi (x)\)  in either the weak- or strong-coupling limit analytically. At weak coupling, a normalizing flow is given by
\(\phi ^{\mathrm {weak}}_i(x) = x_i -\lambda \sum _{j} \left[\frac{1}{2} M^{-1}_{ij} \Lambda _j x^3_j +\frac{3}{4} M^{-1}_{ij} M^{-1}_{jj} \Lambda _j x_j\right]\text{.}\) 
